Fractal characterization of fractured surfaces

Abstract It has recently been claimed [B. B. Mandelbrot, D. E. Passoja and A. J. Pullay, Nature308, 721 (1984)] that fractured surfaces are fractal in nature, i.e. “self similar” over a wide range of scale and that the fractal dimensions of the surfaces correlate well with the toughness of the material. We have investigated these concepts be measuring the fractal dimensions of fractured surfaces of two titanium alloys and attempting to correlate them with dynamic tear energy. We find that, although fractured surfaces can be classified as approximately fractal, the previous conclusions were too optimistic. An approximate correlation between fractal dimension and dynamic tear energy is obtained.